Foxes manager Nigel Pearson insisted his Championship side were not the underdogs heading into the game and he was proved right by his players who dug deep to clinch a quarter-final spot.
The result will be a painful one for Fulham boss Martin Jol whose job becomes more and more in the balance after a uninspiring start to the season.
Hugo Rodallega headed the visitors in front after 18 minutes but Leicester’s resilience meant they went in to the break in front thanks to goals from Wes Morgan and Chris Wood.
Ignasi Miquel headed home eight minutes after the restart to double Leicester’s lead and seemingly put the game to bed before a second goal for Rodallega and a bullet free-kick from Giorgos Karagounis levelled things with just three minutes left on the clock.
But just as the game looked to be heading into extra time, Lloyd Dyer pounced in the 89th minute to hand Leicester the win.
Leicester’s form in the Championship so far this season, compared to Fulham’s in the Premier League, had many touting them for a win. And when Rodallega tapped in a Damien Duff cross mid-way through the first-half it looked as if Fulham might be the ones ready to cause an upset.
But Leicester came to life after going behind and former Fulham defender Paul Konchesky twice went close with long-range efforts for the visitors before Morgan took advantage of Maarten Stekelenburg’s failure to keep hold of a Anthony Kncokaert free-kick to head in the equaliser.
And moments before referee Keith Stroud called time on the first-half, Leicester took the lead through striker Chris Wood with his fourth Capital One Cup goal of the season after Philippe Senderos made a meal of his clearance.
Eight minutes into the second half and Leicester doubled their lead when Ignasi, on loan from Arsenal, got on the end of a Danny Drinkwater cross to nod home his first Foxes goal.
But Fulham got themselves back in straight from the re-start when Elsad Zverotic went unchallenged to cross in for Rodallega’s second goal of the evening.
Leicester looked like they would hold out for a 3-2 victory but Karagounis smashed home an unstoppable free-kick from 25-yards to force a nervy finish and, perhaps, extra-time.
But the prospect of extra-time and penalties did not interest the hosts as they responded perfectly by sending their fans into raptures with a winner two minutes later.
Substitute David Nugent’s first touch of the game played Dyer in who made no mistake with his finish to end this seven-goal thriller.
The last time Leicester beat Fulham in this competition and reached the last-eight they went on to win it in 2000, and they’ll be hoping that kind of coincidence takes them to Wembley this time around.